Resolution of Connicts Involving Many Aircraft via Semideenite Programming

Aircraft con ict detection and resolution is currently attracting the interest of many air transportation service providers and is concerned with the following question: Given a set of airborne aircraft and their intended trajectories, what control strategy should be followed by the pilots and the air tra c service provider to prevent the aircraft from coming too close to each other? This paper addresses this problem by presenting a distributed air-ground architecture, whereby each aircraft proposes its desired heading while a centralized air tra c control architecture resolves any con ict arising between the aircraft involved in the con ict, while minimizing the deviation between desired and con ict-free heading for each aircraft. The resolution architecture relies on a combination of convex programming and randomized searches: It is shown that a version of the planar, multi-aircraft con ict resolution problem that accounts for all possible crossing patterns among aircraft might be recast as a nonconvex, quadratically constrained quadratic program. For this type of problem, there exist e cient numerical relaxations, based on semide nite programming, that provide lower bounds on the best achievable objective. These relaxations also lead to a random search technique to compute feasible, locally optimal and con ict-free strategies. This approach is demonstrated on numerical examples and discussed. Research Assistant, Laboratory for Information and Decision Systems, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139. Research Assistant, Laboratory for Information and Decision Systems, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139. Post-doctoral Associate, Department of Mechanical Engineering, Massachusetts institute of Technology, Cambridge MA 02139 Associate Professor, Senior Member AIAA, Laboratory for Information and Decision Systems, International Center for Air Transportation, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge MA 02139. Author to whom all correspondence should be sent. feron@mit.edu. Paper submitted to the AIAA J. Guidance, Control and Dynamics. Also appeared as a Technical Report, International Center for Air Transportation, MIT, MIT-ICAT 99-5.